The bike is a early 80's Peugeot that appears to have many of the original parts. I put a new chain on the bike and adjusted the gears while on the stand it it seemed to work fine. But, once it got off the stand, I noticed that it was doing a lot of skipping only when I was on the smallest rear cog. It did not make a difference what front chainring was engaged.

The freewheel looks like it's in decent condition, but it that probably the cause of the skipping? It only does it when on the smallest and otherwise the bike seems to shift fine. Reading the other threads on this issue, it sounds like it is the freewheel, but wanted to get an opinion from someone that may have had or seen a similar problem.